On the redundancy of two-dimensional balanced codes

Let A/sub n/spl times/m/ be the set of binary n/spl times/m arrays in which each row, and respectively each column, has the same number of 0's and 1's. We prove the lower bound log/sub 2/|A/sub n/spl times/m/|/spl ges/nm- 1/2 (nlog/sub 2/(2m)+mlog/sub 2/(2n)). We also show that this bound is tight up to an additive term O(n+m).